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Mathematical and Computational Sciences Optimization and Computational Geometry |
Mathematical and Computational Sciences Division Contact: Ronald F. Boisvert Mathematical and computational problems are becoming more elaborate as measurement techniques, physical understanding, and computational capability improve. Solving these problems requires innovative combinations of the methods of modern applied and computational mathematics. In collaboration with other scientists and engineers, we develop and analyze mathematical models of phenomena; design and analyze computational methods and experiments; transform these methods into efficient numerical algorithms for modern, high-performance computers; and validate and extend the models by comparing them with experiments. The research is usually interdisciplinary, requiring expertise in diverse areas of application as well as in mathematical and computational fields. Our staff pursues both short-term consulting and longer-term research collaborations. The resulting interactions often involve collaborations both internal and external to NIST, typically including contributions from researchers in universities and industry. In the course of doing this work, sophisticated problem-solving environments are often developed. Our major research interests include material microstructure, hydrodynamics, electromagnetic and elastic waves, magnetic materials, foams, polymers, machine tool modeling, wireless communications, image analysis, optical reflectance and scattering, and bioinformatics. Frequently occurring mathematical areas include partial differential equations, integral equations, random processes, optimization, non-linear dynamics, inverse problems, and numerical analysis. Contact: Geoffrey B. McFadden The increasing prevalence of computation in science and engineering has generated a need for computer software to solve frequently occurring mathematical and statistical problems. We are actively involved in the development of algorithms for the solution of such problems, as well as in their reliable and maintainable implementation on modern high-performance computers. We undertake specific projects in response to both internal NIST needs and the needs of the computational science community in industry and academia. Recent efforts address such problems as the use of mathematical functions, the adaptive solution of partial differential equations on distributed memory multiprocessors, the solution of large sparse linear systems, and object-oriented numerical software design. The wide dissemination of mathematical reference data and algorithms is one way in which computational science and engineering research is supported. Examples include: the Guide to Available Mathematical Software, a virtual repository of mathematical and statistical software; the Matrix Market, a repository of test data for large sparse linear algebra problems; the Sparse BLAS, a standardized interface for high-performance of linear algebra kernels; and the Digital Library of Mathematical Functions, an online successor to the popular National Bureau of Standards Handbook of Mathematical Functions. Contact: Roldan Pozo Optimization and Computational Geometry Optimization technology is needed whenever a design or a process must be improved or the best among many choices must be identified. For example, it plays an important role in the study of physical systems which naturally select states that minimize energy, or in the design and control of production systems. In some cases, the resulting mathematical problems are discrete and combinatorial in nature. In these cases, a straightforward solution is impractical. Computational geometry involves the solution of problems that are inherently spatial in nature. Examples abound in fields such as robotics, computer aided design, cartography, and computer graphics. We develop optimization and computational geometry methods, applying them to problems of interest to NIST and other government agencies. Examples of such methodology include constrained tetrahedralizations of data sets, surface approximation based upon L1 splines, interior-point techniques and sequential quadratic programming methods for non-convex, non-linear programming problems, and approximate methods for combinatorial counting problems, such as computation of matrix permanents based upon Monte Carlo and importance sampling. These techniques have been applied to areas such as large-scale terrain modeling, thinning of spatial data sets, the first-principle computation of fundamental physical quantities, and the selection of optimal parameters for communication systems. Contact: Ronald F. Boisvert Parallel Computing and Scientific Visualization Computational problems are often so demanding that parallel computing techniques are needed to render them tractable. We use shared-memory multiprocessors and workstation clusters for this purpose. Unfortunately, parallel computing remains a specialized field which typical working scientists and engineers do not have time to master. We develop tools to ease the use of parallel computers and engage in collaborative research projects to improve the performance of applications developed by NIST scientists. Among recently developed tools are WebSubmit, a Web-based tool to ease the submittal of parallel computing jobs, and the Interoperable Message Passing Interface, a standard for communication in heterogeneous computing systems. These tools and others have been applied to the study of optical absorption, fluid flow in porous media, dissipative particle dynamics, and dendritic growth in metallic alloys. Large-scale computations typically lead to enormous collections of output data. Distilling meaningful information from this data is quite difficult. Visualization techniques provide one of the most powerful means of doing this. We work with colleagues in other NIST laboratories to use computer-based scientific graphics for rendering complex experimental, computational, and analytical result. Among the tools we use are vector and raster workstations, photographic and video hardware, high-speed networking for transmitting large graphics data sets between computers and graphics devices, and a variety of specialized visualization software packages. An example of such collaborative work is the visualization of the Bose-Einstein condensate in collaboration with NIST physicists. Contact: Judith
E. Devaney ITL is working with
the NIST Physics and Electronics and Electrical Engineering Laboratories
to develop a measurement and standards infrastructure to support quantum
communications, and to demonstrate and exploit new technologies for quantum
computing. Quantum information networks have the potential of providing
the only known provably secure physical channel for the transfer of information.
The technology has been demonstrated only in laboratory settings, and
a solid measurement and standards infrastructure is needed to move this
into the technology development arena. Quantum computers have potential
for speeding up previously intractable computations. We are supporting
the work in the Physics Laboratory to develop quantum processors and memory,
concentrating on the critical areas of error correction, algorithm and
tool development, and information theory. Contact: Ronald
F. Boisvert
Date
created:October
22, 2001 |